Acoustic turbine

ABSTRACT

A method and apparatus generates kinetic and electrical energy using sound waves and is believed to be particularly useful in high efficiency motors and electrical generators. In particular, the method and apparatus uses sound waves as a catalyst to convert ambient heat energy into kinetic and/or electrical energy. In one embodiment, sound waves at particular frequencies are propagated across one side of a plate or other barrier element, causing flow of fluid (e.g. air) across the surface of the plate which, in turn, causes a reduction in the ambient fluid (air) pressure near the surface of the plate. The difference in fluid pressure on opposite sides of the plate results in net positive thrust on the plate, thereby causing movement of the plate. This movement can be harnessed using, for example, a windmill type of rotor and stator arrangement to generate useful kinetic and electrical energy.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.12/867,736 filed Feb. 16, 2011, entitled “Acoustic Turbine,” which is aU.S. National Phase of PCT/US2009/034313 filed Feb. 17, 2009, whichclaims priority to and the benefit of the filing date of U.S.Provisional Patent Application No. 61/028,974, entitled “AcousticProduction of Kinetic and Electrical Energy,” which was filed on Feb.15, 2008, the entire disclosures of which are hereby incorporated byreference herein.

TECHNICAL FIELD

This application is generally related to the conversion of energy intouseful work, and more specifically is related to a method and apparatusfor converting heat energy into useful kinetic and electrical energyusing acoustic energy.

BACKGROUND OF THE RELATED ART

Sound fields have been used to levitate objects by taking advantage ofthe Boltzmann-Ehrenfest principle of adiabatic invariance, which relatesthe acoustic potential acting on an object positioned in a single-modecavity to a shift in resonant frequency caused by the presence of theobject. In Putterman et al., “Acoustic Levitation and theBoltzmann-Ehrenfest Principle,” J. Acoust. Soc. Am. 85(1), (1989), thetorque imposed on the object in a single mode chamber by acoustic energyequals the angular derivative of the experimentally determined frequencyshift (Δω). However, the levitation technique disclosed in this articleis limited to high frequency sound waves used in single-mode cavities.Further, the created acoustic torque will only align with thecylindrical object being levitated in a horizontal plane, or when θ=90°.These constraints, i.e., high frequency acoustic energy, the single modecavity and the middle horizontal plane, severely limit the applicationsof the disclosed levitation technique.

In an earlier work, Allen et al., “A Powerful High Frequency Siren,” J.Acoust Soc. Am. 19(5), (1947), a high frequency siren is used togenerate chamber pressures of about two atmospheres and an output energyof approximately two kilowatts which can be used for heating purposes.However, this high frequency siren finds little use in most environmentswhere such a sound output would be unacceptable or dangerous.

To date, acoustic or sound energy has not been used effectively toimpart thrust or force on an object for purposes of providing usefulwork. While limited examples of levitation are known, the requirementthat the object being levitated be disposed in an enclosed chamberrenders the technique largely inapplicable. Further, the use of powerfulsirens for generating heat is also largely industrially inapplicable andpotentially harmful to workers.

SUMMARY OF THE DISCLOSURE

A method and apparatus that generate kinetic and electrical energy usingsound waves is believed to be particularly useful in high efficiencymotors and electrical generators. Stated simply, the method andapparatus described herein use sound waves as a catalyst to convertambient heat energy into kinetic and/or electrical energy.

In one embodiment, sound waves at particular frequencies are propagatedacross one side of a plate or other barrier element, causing flow offluid (e.g. air) across the surface of the plate which, in turn, causesa reduction in the ambient fluid (air) pressure near the surface of theplate. The difference in fluid pressure on opposite sides of the plateresults in net positive thrust on the plate, thereby causing movement ofthe plate. This movement can be harnessed using, for example, a windmilltype of rotor and stator arrangement to generate useful kinetic andelectrical energy.

In another embodiment, a sonic thrust apparatus includes a barrierelement including a first outer surface and a second outer surface. Thesonic thrust apparatus further includes an acoustic oscillator disposedin close proximity to the first outer surface of the barrier element.The sonic thrust apparatus further includes a drive mechanism drivingthe acoustic oscillator to produce sound waves flowing along the firstouter surface to create a pressure differential between the first outersurface and the second outer surface and to create a thrust on thesecond outer surface towards the first outer surface.

In yet another embodiment an acoustic turbine includes a rotor having anaxis of rotation and at least one lever arm coupled to the rotor andextending way from the rotor. The lever arm includes a thrust elementdisposed on the lever arm. The thrust element may include a barrierelement including a first outer surface and a second outer surface, andmay further include an acoustic oscillator disposed in close proximityto the first outer surface of the barrier element. The thrust elementmay also include a drive mechanism for driving the acoustic oscillatorto produce sound waves flowing along the first outer surface to create apressure differential between the first outer surface and the secondouter surface and to create a thrust on the second outer surface towardsthe first outer surface to rotate the rotor.

The operating principle of this system is analogous to the forces thatresult in lift on an airplane wing, in which faster air flow over thetop of the wing, as compared to slower air flow over the bottom of thewing, causes a pressure difference on the opposite sides of the wingwhich, in turn, causes lift. Consistent with Bernoulli's law (whichpredicts the lift of an airplane wing), a sonic oscillator, properlyconfigured, produces sound waves that result in a pressure drop on oneside of the plate or other barrier element as compared to the oppositeside of the plate or barrier element. This pressure difference resultsin enough thrust to turn a mechanical gear or other rotating mechanism.This system and method can therefore be used as part of a motor toproduce rotation, or as part of a generator to generate electricalenergy.

The kinetic and electrical energy generated by this system and method isultimately derived from the heat energy in the ambient fluid (air), aspredicted by the ideal gas law, and preliminary research predicts thatthis energy conversion can be performed with surprisingly highefficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a sonic thrust element which uses sonicenergy to produce thrust on a barrier element in the form of a flatplate;

FIG. 2A is a perspective view of a sonic thrust element that includes amotor system for oscillating the acoustic oscillator in FIG. 1;

FIG. 2B is a cross-sectional view of the sonic thrust element in FIG.2A;

FIG. 3 is a perspective view of a sonic motor having multiple sonicthrust elements disposed on a rotor to produce useful kinetic energy;and

FIG. 4 is a cross-sectional, side view of a second embodiment of a sonicthrust element which uses sonic energy to produce thrust on a barrierelement in the form of a flat plate.

DETAILED DESCRIPTION

Generally speaking, sound can be used as a catalyst for obtaining torqueon a barrier element, such as a flat plate, which thereby causes motionof the plate. When connected to proper mechanical structures, such as alever arm connected to a rotatable axis, the motion of the plate can beconverted into useful kinetic energy to drive a rotating wheel, gear,bar or other element. This motion can also be converted into electricalenergy using an electrical rotor and stator configuration as is commonin well known generator technology.

In a simple form, an acoustic oscillator is used to generate and directsound waves across the surface of a barrier element in the form of aflat plate. The sound waves, when properly generated, form a lowpressure region immediately adjacent to the surface of the flat plate atwhich the acoustic oscillator is located. Ambient fluid pressure on theother side of the plate results in thrust on the plate, which propelsthe plate toward the low pressure region, and this thrust can beharnessed to produce useful kinetic and electrical energy.

FIG. 1 illustrates an example of a sonic thrust element 5 including aflat plate 10 having an upper surface 12 and a lower surface 14, and anacoustic oscillator 20 disposed in close proximity to the upper surface12 of the flat plate 10. In particular, the acoustic oscillator 20 isillustrated as a square oscillator disposed slightly above, and in themiddle of the upper surface of the flat plate 10. In this case, theoscillator 20 is disposed a finite distance ε above the upper surface 12of the flat plate 10 and is positioned so as to produce sound waves thatflow across the upper surface 12 of the flat plate 10 in a directiongenerally perpendicular to the normal of the flat plate 10. The arrows25A and 25B indicate the direction of sound propagation in the system ofFIG. 1.

During operation, electrical or other energy (such as mechanical energy)is provided to drive the acoustic oscillator 20 (via electrical wires orother mechanical mechanism not shown in FIG. 1) so that the acousticoscillator 20 produces sound waves, having a constant or near constantfrequency as described in more detail below. These sound waves propagateacross the upper surface 12 of the flat plate 10 on either sides of theoscillator 20, as illustrated by the arrows 25A and 25B. If produced inaccordance with the techniques and constraints defined herein, the soundwaves produced by the oscillator 20 create a low pressure regionimmediately adjacent to the upper surface 12 of the flat plate 10. Asthe sound waves produced by the oscillator 20 do not affect the fluidpressure immediately adjacent the flat plate 10 on the lower surface 14of the flat plate 10, a pressure differential is created on the oppositesides 12 and 14 of the flat plate 10. This pressure differential resultsin a thrust (denoted by arrows 26) on the lower surface 14 of the flatplate 10, across the entire surface 14 of the flat plate 10, andgenerally in the direction of the upper surface 12 of the flat plate 10.

FIGS. 2A-2B illustrate another example of a sonic thrust element 7including a flat plate 10 having an upper surface 12 and a lower surface14, and an acoustic oscillator 20 disposed in close proximity to theupper surface 12 of the flat plate 10. In this case, the flat plate 10includes an aperture 60 (e.g., a hole, or a slit), and the oscillator 20is coupled to a motor system 50 via the aperture 60. The motor system 50linearly oscillates (drives) the oscillator back and forth along theplane of the upper surface 12 so that the acoustic oscillator 20produces sound waves, having a constant frequency as described in moredetail below. As explained in reference to FIG. 1, these sound wavespropagate across the upper surface 12 of the flat plate 10 and create apressure differential on the opposite sides 12 and 14 of the flat plate10 that results in a thrust on the lower surface 14 of the flat plate10, and generally in the direction of the upper surface 12 of the flatplate 10 (i.e., in the direction normal to the surface plane of the flatplate 10).

The motor system 50 may be implemented in a number of ways. For example,a rotational motor may be used (not shown). The rotational motor may becoupled to a linkage, a cam, etc., to transform the rotational motion ofthe rotational motor into a linear motion along the upper surface 12 ofthe flat plate 10. In some embodiments, the rotational motion and/or theresulting linear motion have an associated frequency of 450 Hz.

The motor system 50 may be coupled to the acoustic oscillator 20 in anyof a variety of manners (e.g., via bolts, nuts, pins, cams, linkagearms, and so on). In some embodiments, the motor system 50 may be easilydetachable from the acoustic oscillator 20 so that different motorsystems may be used. Moreover, the motor system 50 may take the form of,or may be powered by mechanical motion collected from other sources,such as sources of waste heat or waste energy.

In different embodiments, the different building blocks of the sonicthrust element 7 may be of different shapes and sizes and may be madefrom a variety of materials. For example, the flat plate 10 may be asquare plate, 500 mm on each side. The acoustic oscillator 20 may have awidth of 500 mm, and a height and length of 38.1 mm. The aperture in theflat plate 10 may be 88 mm thereby allowing the oscillator 20 tooscillate 88 mm along the flat plate 10. Both the flat plate 10 and theoscillator 20 may be may be made of aluminum. However, the flat plate 10and/or the oscillator 20 may be made of other suitable materials, suchas carbon fiber, fiberglass, etc. Of course, these materials, and systemdimensions are associated with one particular embodiment of theinvention, and other sets of dimensions and materials will operateaccording to the principles described herein. Thus, the invention is notlimited to the particular dimensions and materials described herein withrespect to FIG. 2.

FIG. 3 illustrates a motor 27 (referred to herein as a sonic motor)which can harness the thrust on the flat plate 10 of FIG. 1 to produceuseful kinetic energy. In particular, the motor 27 of FIG. 3 includes arotor 28 having, in this case, four lever arms 30 rigidly connected toand disposed around a center bar 32. The bar 32 rotates about alongitudinal axis 34 which defines an axis of rotation for the rotor 28.As illustrated in FIG. 3, thrust elements 5 (described with respect toFIG. 1) are disposed on the ends of the lever arms 30 so that the plates10 of the thrust elements 5 are disposed extending out from the leverarms 30 in an essentially radial plane with respect to the axis ofrotation 34 and/or so that a normal to the surface of the plane of eachof the flat plates 10 is disposed in an essentially tangential directionwith respect to a circle disposed in a plane perpendicular to the axisof rotation 34 and having a center point on the axis of rotation 34.

While the oscillators 20 of the thrust elements 5 are illustrated asbeing disposed to extend radially out from the axis of rotation 34, thethrust elements 5 could be rotated so that the acoustic oscillators 20extend in any other direction with respect to the axis of rotation 34.Thus, for example, instead of being disposed horizontally across theplates 10 from side to side, as illustrated in FIG. 3, the oscillators20 could be disposed vertically across the plates 10 (from top tobottom), or an any diagonal direction across the plates 10. Stillfurther, while each of the oscillators 20 is illustrated as beingdisposed across a center of one of the flat plates 10, the oscillator 20of the thrust elements 5 could be disposed, instead, off-center withrespect to an associated flat plate 10, and even at the edge of the flatplate 10, if so desired, as long as the oscillator 20 directs soundwaves across the top surface 12 of the associated flat plate 10.Moreover, while the flat plates 10 are illustrated as essentially squareplates, the plates 10 could be other shapes as well, such asrectangular, circular, oval, etc. Also, while the surface 14 of the flatplates 10 is illustrated as being flat, this condition may not benecessary, and other surface contours could be used as well. Likewise,while four sonic thrust elements 5 are shown in FIG. 3 as beingconnected to the center bar 32 via lever arms 30, any other number ofthrust elements 5, such as one, two, three, five, etc. could be usedinstead.

In the structure of FIG. 3, operation (energization) of the oscillators20 causes thrust on the flat plates 10, which thrust is illustrated bythe arrows 36 in FIG. 3. The thrust 36 on the flat plates 10 places atorque on the lever arms 30 proportional to the lengths of the arms 30,and imparts a rotational thrust 38 onto the bar 32 around the axis ofrotation 34. The bar 32 may be allowed to rotate and, if desired, may beconnected to a gearing mechanism 40 which can be used to harness therotational kinetic energy imparted to the bar 32 by the sonic thrustelements 5. If desired, this kinetic energy may be converted toelectrical energy with the use of a generator (not shown in FIG. 3). Insuch an embodiment, the rotor 28 may have an electromagnetic fieldelement which creates a rotating electromagnetic field with respect to(e.g., inside of or around) a stator, which may generate electricity inthe stator. As generators are well known, they will not be described inmore detail herein.

Generally speaking, the operation of the sonic thrust elements 5 ofFIGS. 1, 2 and 3 can be more completely understood on the basis of ananalogy to the force imparted to an airplane wing moving with subsonicspeed through the air (an ambient fluid). In this case, the shape of thewing causes the pressure above the wing to be less than the pressurebelow the wing as the wing moves through the air, in the mannerpredicted by Bernoulli's law, which in turn causes lift on the wing. Inthe case of the structures of FIGS. 1, 2 and 3, the airplane wing isreplaced by a plate 10 having an acoustic oscillator disposed on oneside of the plate 10. The sound waves generated by the oscillators 20mimic air flowing at the speed of sound over the surface of the plate10. According to Bernoulli's law, the pressure on the surface of theplate 10 over which the sound waves are traveling will be less than thepressure on the opposite side of the plate 10. Based on the timedependent version of Bernoulli's law, a thrust on the plate 10 results.However, in order for this thrust to occur as a result of the soundwaves produced by the oscillator 20, a number of conditions must besatisfied based on the mathematical derivations of the physicalprinciples occurring in this system.

To begin with, a number of basic variables used in the equations beloware defined as:

-   -   L is the length of the plate (10);    -   S is the width of the plate (10);    -   H is the height of the oscillator (20), from the bottom of the        oscillator near the plate surface (12) to the top of the        oscillator;    -   ε is the distance from the bottom of the oscillator to the top        of the plate;    -   α is the length of the rotation arm, defined as the distance        between the axis of rotation (34) and the center of mass of (a)        the rotating arm (30) plus (b) the plate plus (c) the        oscillator; and    -   C is the speed of sound in the ambient fluid.        First the wattage output of an acoustic oscillator can be        expressed as:

$\begin{matrix}{{W({watts})} = {\Omega = {\frac{256\mspace{14mu}\pi^{3}\delta\;{SHA}^{3}}{2^{\frac{5}{2}}}\frac{1}{{cm}^{6}}}}} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$

-   -   wherein:    -   W is the output of the oscillator in watts;    -   δ is the mass density of the ambient fluid;    -   H is the height of the oscillating diaphragm;    -   S is the width of the oscillating diaphragm (also the width of        the plate); and    -   A is the amplitude of the oscillation measured in cm/s.        It is well known that a watt is:

-   Watt=10⁷ dyn-cm/s=10⁷ g-cm²/s³

Next, the formula for the optimal thrust (T) on a flat plate due to anacoustic source acting as a catalyst, such as that illustrated in FIG.1, can be expressed as:

$\begin{matrix}{T = {\frac{\pi\;\delta\; A^{2}\;\cos^{2}\;( {2\;\pi\;{ft}} )}{ɛ^{2}} + \frac{8\;\pi\;\delta\; S\sqrt{\frac{LS}{\pi}}{{HA}( {2\;\pi\; f} )}\;\sin\;( {2\;\pi\;{ft}} )}{{cm}^{2}}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$

-   -   wherein:    -   f is the frequency of the sound waves created by the oscillator        in hertz;    -   t is the time in seconds;    -   ε is the distance from the bottom of the oscillator to the top        of the plate;    -   δ is the mass density of the ambient fluid.        However, for the system of FIG. 1 to operate, the thrust on the        plate 10 must point in one direction only, that is, from the        lower side 14 of the plate 10 to the upper side 12 of the plate        10 as illustrated in FIG. 1. To meet this condition, the second        part of the expression on the right side of Eq. (2) must be able        to be ignored (i.e., must be much less than the first part),        which occurs when:

$\begin{matrix}{{\frac{A}{32\sqrt{\pi}S^{\frac{3}{2}}{HL}^{\frac{1}{2}}ɛ^{2}}{cm}^{2}}\operatorname{>>}\; f} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$wherein >> means at least a magnitude of 10 times greater than.

-   This formula was obtained using:

$\begin{matrix}{< {\cos^{2}2\pi\;{ft}}>=\frac{1}{2}} & {{Eq}.\mspace{14mu}(4)}\end{matrix}$wherein <quantity> means the average value of the quantity over onecycle and setting the sine term in the second part of the expression onthe right side of Eq. (2) equal to 1.

Now, at optimal thrust conditions, the fluid pressure on the oscillatorside of the plate is near a vacuum, and so, at this condition, thethrust T on the plate is:T=PLS  Eq. (5)

-   -   wherein:    -   T is the thrust on the plate;    -   P is the ambient fluid pressure on the non-oscillator side of        the plate;    -   L is the length of the plate; and    -   S is the width of the plate.

Substituting Eq. (4) into Eq. (2) assuming that the constraint of Eq.(3) is satisfied gives:

$\begin{matrix}{T = \frac{\pi\;\delta\; A^{2}}{2\; ɛ^{2}}} & {{Eq}.\mspace{14mu}(6)}\end{matrix}$and equating the different expressions for the thrust T from Eqs. (6)and (5) gives:

$\begin{matrix}{T = {\frac{\pi\;\delta\; A^{2}}{2\; ɛ^{2}} = {PLS}}} & {{Eq}.\mspace{14mu}(7)}\end{matrix}$Expressing the right most equality of Eq. (7) as a function of ε (thedistance from the bottom of the oscillator to the top surface of theplate) gives:

$\begin{matrix}{ɛ = \frac{\sqrt{\pi/2}\delta^{\frac{1}{2}}A}{P^{\frac{1}{2}}L^{\frac{1}{2}}S^{\frac{1}{2}}}} & {{Eq}.\mspace{14mu}(8)}\end{matrix}$Now, the torque G produced by a single plate in a rotor system such asthat of FIG. 3 at the optimal thrust conditions is expressed as:

$\begin{matrix}{G = {{{PLS}\;\alpha} = \frac{\pi\;\delta\; A^{2}\alpha}{2\; ɛ^{2}}}} & {{Eq}.\mspace{14mu}(9)}\end{matrix}$From the discussion above, Eqs. (3) and (8) are constraints that must besatisfied when operating the system, wherein Eq. (3) guarantees that thethrust on the plate is always directed from the side of the plateopposite the acoustic oscillator towards the side of the plate with theacoustic oscillator and Eq. (8) is a condition for optimal thrust.

Of course, there is a physical limit to how close the oscillator 20 canbe placed to the side 12 of the plate 10, and thus there is a physicallimit to how small ε can be made. A reasonable choice for minimalpossible value of ε is believed to be about 3×10⁻⁶ cm (i.e., 300angstroms) as films of plastics such as collodion can be manufactured atthis thickness to be used as windows for low pressure gas retention.Substituting this value for ε into Eq. (8) gives:

$\begin{matrix}{\frac{\pi\;\delta\; A^{2}}{2\;{PLS}} \geq {9 \times 10^{- 12}{cm}^{2}}} & {{Eq}.\mspace{14mu}(10)}\end{matrix}$

Next, in order to justify neglecting the viscosity terms in theNavier-Stokes equations for the ambient fluid, the following constraintis also determined:

$\begin{matrix}{\frac{3\;\delta\; C^{3}}{8\;\pi^{2}\mu\; H}\operatorname{>>}\; f^{\mspace{11mu} 2}} & {{Eq}.\mspace{14mu}(11)}\end{matrix}$

-   -   wherein:    -   C is the speed of sound in the ambient fluid; and    -   μ is the absolute viscosity of the ambient fluid.        Substituting the ideal gas law (P=ρRT_(emp)) into Eq. (8) gives:

$\begin{matrix}{ɛ = \frac{\sqrt{\pi/2}\delta^{\frac{1}{2}}A}{\rho^{\frac{1}{2}}R^{\frac{1}{2}}T_{emp}^{\frac{1}{2}}L^{\frac{1}{2}}S^{\frac{1}{2}}}} & {{Eq}.\mspace{14mu}(12)}\end{matrix}$

-   -   wherein:    -   ρ is the weight density of the gas;    -   R is the gas constant; and    -   T_(emp) is temperature.        Eq. (12) relates the optimal thrust to the temperature of the        gas (ambient fluid). As can be seen, as the density of the gas        varies, δ/ρ remains constant, meaning that there is a direct        dependence of ε on the temperature T_(emp) and thus that the        energy which produces the thrust in this system comes from the        heat in the ambient fluid.

A final constraint that must be satisfied is:

$\begin{matrix}{f\operatorname{>>}\frac{C}{\sqrt{\pi\;{LS}}}} & {{Eq}.\mspace{14mu}(13)}\end{matrix}$This constraint assures that the wavelength of the sound waves are smallcompared to the dimensions of the plate, so that the sound waves behavelike particles traveling near the speed of sound (thereby justifying theairplane wing analogy).

Now, it is possible to describe the thrust on the plate in terms of thewattage output of the oscillator as:

$\begin{matrix}{T = {\frac{581.7\mspace{14mu}\Omega^{\frac{2}{3}}\delta^{\frac{1}{3}}}{ɛ^{2}S^{\frac{2}{3}}H^{\frac{2}{3}}}\frac{g^{\frac{2}{3}}{cm}^{\frac{16}{3}}}{s^{2}}}} & {{Eq}.\mspace{14mu}(14)}\end{matrix}$Thus, expressed in terms of the wattage output of the oscillator fromEq. (14), the constraints which must be satisfied to obtain optimalthrust on the plate using sound waves are:

$\begin{matrix}{{Constraint}\mspace{14mu} 1} & \; \\{{\frac{5.833 \times 10^{- 4}{PL}^{\frac{1}{2}}}{\delta^{\frac{2}{3}}S^{\frac{1}{6}}H^{\frac{2}{3}}\Omega^{\frac{1}{3}}}\frac{s}{g^{\frac{1}{3}}{cm}^{\frac{2}{3}}}}\operatorname{>>}f} & ( {C\; 1} )\end{matrix}$

This constraint is derived by solving the right most equality of Eq. (1)for A and substituting this expression of A into Eq. (3).

$\begin{matrix}{{Constraint}\mspace{14mu} 2} & \; \\{ɛ = {\frac{24.12\mspace{14mu}\Omega^{\frac{1}{3}}\delta^{\frac{1}{6}}}{P^{\frac{1}{2}}L^{\frac{1}{2}}S^{\frac{5}{6}}H^{\frac{1}{3}}}\frac{g^{\frac{1}{3}}{cm}^{\frac{8}{3}}}{s}}} & ( {C\; 2} )\end{matrix}$

This constraint is derived by solving the right most equality of Eq. (1)for A and substituting this expression of A into Eq. (8).Constraint 3:ε≧3×10⁻⁶ cm  (C3)

Assumption based on reasonable expectation of physical limits

$\begin{matrix}{{Constraint}\mspace{14mu} 4} & \; \\{{\frac{5.817\mspace{14mu}\Omega^{\frac{2}{3}}\delta^{\frac{1}{3}}}{{PLS}^{\frac{5}{3}}H^{\frac{2}{3}}}\frac{g^{\frac{2}{3}}{cm}^{\frac{16}{3}}}{s^{2}}} \geq {9 \times 10^{- 14}{cm}^{2}}} & ( {C\; 4} )\end{matrix}$

This constraint is determined by plugging the ε value of C2 into C3.

$\begin{matrix}{{Constraint}\mspace{14mu} 5} & \; \\{\frac{3.80 \times 10^{- 2}\delta\; C^{3}}{\mu\; H}\operatorname{>>}\; f^{\; 2}} & ( {C\; 5} )\end{matrix}$

The constraint of Eq. (11).

$\begin{matrix}{{Constraint}\mspace{14mu} 6} & \; \\{f\operatorname{>>}\frac{0.564\mspace{14mu} C}{L^{\frac{1}{2}}S^{\frac{1}{2}}}} & ( {C\; 6} )\end{matrix}$

The constraint of Eq. (13).

Now, assuming that the physical parameters (L, S, H, ε, f, etc.) can bechosen such that these conditions (C1-C6) can be met, the rotationaltorque G that will be produced by a single plate element (i.e., a singlesonic thrust element 5 of FIG. 1) attached to an arm is:

$\begin{matrix}{G = {{\frac{{581.7\mspace{14mu}\Omega^{\frac{2}{3}}\delta^{\frac{1}{3}}\alpha}\;}{ɛ^{2}S^{\frac{2}{3}}H^{\frac{2}{3}}}\frac{g^{\frac{2}{3}}{cm}^{\frac{16}{3}}}{s^{2}}} = {{PLS}\;\alpha}}} & {{Eq}.\mspace{14mu}(15)}\end{matrix}$

This equation is derived by solving the right most equality of Eq. (1)for A and substituting this expression of A into Eq. (9).

From Eq. (15), the power output (PO) of the rotating plate system with asingle plate or thrust element is:

$\begin{matrix}{{P\; O} = {\frac{{.1047}\mspace{14mu}( {\# R_{m}} )\alpha\;{PLS}}{s} = {2\;\pi\; R_{ps}G}}} & {{Eq}.\mspace{14mu}(16)}\end{matrix}$

-   -   wherein:    -   R_(ps) is the number of revolutions of the arm per second; and    -   #R_(m) is the number of revolutions of the arm in one minute        such that R_(ps)=#R_(m)/60 s.

COMPUTATIONAL EXAMPLE

An explicit example of the parameters of the system described above isprovided below illustrating that all of the constraints (C1-C6) can besimultaneously satisfied. In this example, the ambient fluid is taken tobe air at 69 deg F. at standard atmospheric pressure. As such, and as isknown for this condition:μ=0.00018 g/cm-s (the absolute viscosity of air).P=1.013×10⁶ g/cm-s² (the ambient air pressure).ρ=1.1781 g/cm²-s² (the weight density of ambient air).δ=1.2013×10⁻³ g/cm³ (the mass density of ambient air).C=33162 cm/s (the speed of sound in ambient air).

The dimensions of the plate and the oscillating diaphragm in thisexample are taken to be:L=60 cmS=10 cmH=5 cm.Moreover,α=60 cm (the length of the rotation arm);Ω=0.25 watts (the output wattage of the acoustic oscillator); andf=16000 hertz=16000/s (the frequency of oscillation of the oscillator).

For this example, it will be assumed that the acoustic oscillator is ¼percent efficient, which is a reasonable assumption, and that the inputwattage to the oscillator is 100 watts, which is reasonably attainablewith common acoustic speakers.

Substituting these values into the constraints (C1-C6) and solving forthese equations provides the following expressions.1.625×10⁵/s>>16000/s  C1:ε=5.454×10⁻⁵ cm  C2:5.454×10⁻⁵ cm≧3×10⁻⁶ cm  C3:2.975×10⁻¹¹ cm≧9×10⁻¹⁴ cm  C4:9.25×10¹²/s²>>2.56×10⁸/s²  C5:1.6×10⁴/s>>7.636×10²/s  C6:

Thus, all of the constraints defined by C1-C6 are satisfied, and thesystem manufactured and operated with these conditions will thereforeoperate as described. Of course, many other choices of the variables L,S, H, α, and f will work as well, and the operation of the systemdescribed herein is certainly not limited to the specific computationalexample described herein.

The described system does not violate the principles of the conversationof energy, and the underlying operation of the system instead, isconsistent with the principle of conservation of energy as the energycomes from the heat in the ambient fluid. Generally speaking, the sonicthrust element described herein produces a low pressure region on theside of the plate where the oscillator is located while keeping standardatmospheric pressure on the other side of the plate. By restricting thewavelength of the sound waves to be small compared to the dimensions ofthe plate, the sound waves behave like particles moving at nearly thespeed of sound. The analogy with the flow of air across an airplane wingis thus very strong and Bernoulli's law in fact predicts a thrust thatis close to that of standard atmospheric pressure against a vacuum Thepressure differences are directly related to temperature differences,and hence to energy differences. Stated another way, Bernoulli's law,which predicts the pressure difference on the opposite sides of theplate, combined with the ideal gas law, which predicts a temperaturechange with pressure change, means that the heat energy in the air isconverted into the kinetic energy in the moving plate and lever armdevice. Thus, the sound waves are not converted into to kinetic energydirectly, but serve as a catalyst for converting heat energy in theambient fluid (e.g., air) into kinetic energy.

It is possible to modify the sonic thrust element 5 of FIG. 1 to reduceor eliminate the need to account for the finite distance ε between thebottom of the oscillator 20 and the top of the plate 10 in the equationsabove. In particular, the oscillator 20 can be disposed partially downwithin the plate 10 to assure sound waves emanate from the oscillator 20at the same level as the top surface 12 of the flat plate 10, so thatthere is no distance between the “bottom of the oscillator” and the topof the flat plate 10.

FIG. 4 illustrates one example of such a configuration. Here, the plate10 is illustrated as including a top portion 10A and a bottom portion10B connected by side portions 10C forming a hollow section 102 betweenthe top and bottom portions 10A and 10B of the plate 10. The oscillator20 extends from above the top portion 10A of the plate 10 down into thehollow section 102 of the plate 10 through a hole or slit 104 such thatthe bottom of the oscillator 20 is at the same level as or below the topsurface 12 of the top portion 10A of the plate 10. A control mechanism106 is illustrated diagrammatically in FIG. 4 as being attached to theoscillator 20 to operate the oscillator 20 to produce sound waves of,for example, a constant frequency as defined by the constraintsdescribed herein. The mechanism 106 may be electrical or mechanical innature using any standard oscillator technology. Moreover, if desired,the control mechanism 106 may be at least partially disposed within thehollow section 102 of the plate 10.

Using the sonic thrust element illustrated in FIG. 4 eliminates the needfor Eq. (12) and the constraints (C2) (C3) and (C4) given above for thesonic thrust element 5 of FIG. 1. This configuration is thus left with asmaller set of constraints given as:

$\begin{matrix}{{\frac{5.833 \times 10^{- 4}{PL}^{\frac{1}{2}}}{\delta^{\frac{2}{3}}S^{\frac{1}{6}}H^{\frac{2}{3}}\Omega^{\frac{1}{3}}}\frac{s}{g^{\frac{1}{3}}{cm}^{\frac{2}{3}}}}\operatorname{>>}f} & ( {C\; 1^{\prime}} ) \\{\frac{3.80 \times 10^{- 2}\delta\; C^{3}}{\mu\; H}\operatorname{>>}\; f^{2}} & ( {C\; 2^{\prime}} ) \\{f\operatorname{>>}\frac{0.564\mspace{14mu} C}{L^{\frac{1}{2}}S^{\frac{1}{2}}}} & ( {C\; 3^{\prime}} )\end{matrix}$As before, for a single arm rotational device using the thrust elementof FIG. 3:

G = α PLS and${P\; O} = {\frac{{.1047} \times ( {\# R_{m}} )\alpha\;{PLS}}{s}.}$

Again, if the ambient fluid is taken to be air at 69 deg F. at standardatmospheric pressure, then:μ=0.00018 g/cm-s (the absolute viscosity of air).P=1.013×10⁶ g/cm-s² (the ambient air pressure).ρ=1.1781 g/cm²-s² (the weight density of ambient air).δ=1.2013×10⁻³ g/cm³ (the mass density of ambient air).C=33162 cm/s (the speed of sound in ambient air).

Plugging these values into the constraints (C1′), (C2′) and (C3′) givesthe specific constraints:

$\begin{matrix}{{\frac{5.229 \times 10^{4}L^{\frac{1}{2}}}{S^{\frac{1}{6}}H^{\frac{2}{3}}\Omega^{\frac{1}{3}}}\frac{{cm}^{\frac{1}{3}}}{s}}\operatorname{>>}f} & ( {C\; 1^{\prime}} ) \\{{\frac{9.249 \times 10^{12}}{H}\frac{cm}{s^{2}}}\operatorname{>>}f^{\; 2}} & ( {C\; 2^{\prime}} ) \\{{f\operatorname{>>}{\frac{1.870 \times 10^{4}}{L^{\frac{1}{2}}S^{\frac{1}{2}}}\frac{cm}{s}}}{and}{{P\; O} = {\frac{1.0606 \times 10^{5}\mspace{11mu}( {\# R_{m}} )\alpha\;{LSg}}{{cm}\mspace{14mu} s^{3}}.}}} & ( {C\; 3^{\prime}} )\end{matrix}$

A number of examples using this configuration will now be provided, itbeing understood that other example configuration parameters can be usedas well or instead.

Example 1

α=1000 cmL=100 cmS=100 cmH=10 cm#R _(m)=100Ω=1 watt.In this example, the constraints (C1′)-(C3′) become:

$\frac{5.229 \times 10^{4}}{s}\operatorname{>>}f$$\frac{9.249 \times 10^{11}}{s^{2}}\operatorname{>>}f^{\; 2}$$f\operatorname{>>}\frac{1.870 \times 10^{2}}{s}$and these constraints may be consistently satisfied for f=2×10³ hertz.

Example 2

α=100 cmL=20 cmS=5 cmH=1 cm#R _(m)=100Ω=0.25 watt.In this example, the constraints (C1′)-(C3′) become:

$\frac{2.253 \times 10^{5}}{s}\operatorname{>>}f$$\frac{9.249 \times 10^{12}}{s^{2}}\operatorname{>>}f^{\mspace{11mu} 2}$$f\operatorname{>>}\frac{1.870 \times 10^{3}}{s}$and these constraints may be consistently satisfied for f=2×10⁴ hertz.

Example 3

α=5 cmL=2.5 cmS=2 cmH=0.5 cm#R _(m)=40Ω=0.001 watt.In this example, the constraints (C1′)-(C3′) become:

$\frac{1.169 \times 10^{6}}{s}\operatorname{>>}f$$\frac{1.850 \times 10^{13}}{s^{2}}\operatorname{>>}f^{\mspace{11mu} 2}$$f\operatorname{>>}\frac{8.364 \times 10^{3}}{s}$and these constraints may be consistently satisfied for f=10⁵ hertz.

While the present invention has been described with reference tospecific examples, which are intended to be illustrative only and not tobe limiting of the invention, it will be apparent to those of ordinaryskill in the art that changes, additions or deletions may be made to thedisclosed embodiments without departing from the spirit and scope of theinvention.

What is claimed is:
 1. An acoustic turbine comprising: a rotor having anaxis of rotation; and at least one lever arm coupled to the rotor andextending away from the rotor, the lever arm including a thrust elementdisposed on the lever arm, the thrust element comprising: a barrierelement including a first outer surface and a second outer surface; anacoustic oscillator disposed in close proximity to the first outersurface of the barrier element; and a drive mechanism for driving theacoustic oscillator to produce sound waves flowing along the first outersurface to create a pressure differential between the first outersurface and the second outer surface such that the pressure on the firstouter surface is less than the pressure on the second outer surface andthereby to create a thrust on the second outer surface towards the firstouter surface, the thrust having a component that is orthogonal to theaxis of rotation to rotate the rotor.
 2. The acoustic turbine of claim1, wherein the at least one lever arm comprises two lever arms coupledto the rotor and extending from the rotor in opposite directions.
 3. Theacoustic turbine of claim 1, wherein the barrier element is a flat plateand wherein the first outer surface is substantially parallel to thesecond outer surface.
 4. The acoustic turbine of claim 1, wherein thedrive mechanism drives the acoustic oscillator to produce sound waveshaving a substantially constant frequency.
 5. The acoustic turbine ofclaim 4, wherein the substantially constant frequency (f) is constrainedby:${f{\operatorname{<<}\frac{A}{32\sqrt{\pi}S^{\frac{3}{2}}{HL}^{\frac{1}{2}}ɛ^{2}}}{cm}^{2}},{f^{2}{\operatorname{<<}\frac{3\;\delta\; C^{3}}{8\;\pi^{2}\mu\; H}}},{and}$${f\operatorname{>>}\frac{C}{\sqrt{{\pi\;{LS}}\;}}},$ wherein A is theamplitude of oscillation, S is a width of the acoustic oscillator, H isa height of the acoustic oscillator, L is a length of the acousticoscillator, ε is a distance between a surface of the acoustic oscillatorand the first outer surface of the barrier element, δ is a mass densityof ambient fluid, C is the speed of sound in ambient fluid, μ isabsolute viscosity of ambient fluid, << indicates at least a magnitudeof ten times less than and >> indicates at least a magnitude of tentimes greater than.